Of course believing is not a work. All a sinner must do to be saved is to believe on Jesus.Believing is a work because its something we do Rom 10:9
9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
Believe here is in the active voice which:
Represents the subject as the doer or performer of the action. e.g., in the sentence, "Jesus returned to Capernaum" Jesus performs the action.
Again a work by definition, the greek word ergon:
- any product whatever, any thing accomplished by hand, art, industry, or mind
- an act, deed, thing done: the idea of working is emphasised in opp. to that which is less than work
Also To believe is a work of mental ability of the mind and ; the understanding, and the will, conscience and affections. Paul wrote of receiving the Love of the Truth 2 Thess 2:10
And with all deceivableness of unrighteousness in them that perish; because they received not the love of the truth, that they might be saved.
So If I say Im saved because I believed, God saved me because I performed that action, thats Salvation by my works, even if we count it as a work of righteousness, what does Titus 3:5 say
5 Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;